The normality of the residuals is important in the inference procedures for
the classical linear regression model, and normality is very important in
correlation analysis (second moment)...
Washington S. Silva
Thank you all for your replies they have been more useful... well
in my case I have chosen to do some parametric tests (more precisely
correlation and linear regressions among some variables)... so it
would be nice if I had an extra bit of support on my decisions... If I
understood well from all your replies... I shouldn't pay s much
attntion on the normality tests, so it wouldn't matter which one/ones
I use to report... but rather focus on issues such as the power of the
test...
Thanks again.
On 25/05/07, Lucke, Joseph F [EMAIL PROTECTED] wrote:
Most standard tests, such as t-tests and ANOVA, are fairly resistant to
non-normalilty for significance testing. It's the sample means that have
to be normal, not the data. The CLT kicks in fairly quickly. Testing
for normality prior to choosing a test statistic is generally not a good
idea.
-Original Message-
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of Liaw, Andy
Sent: Friday, May 25, 2007 12:04 PM
To: [EMAIL PROTECTED]; Frank E Harrell Jr
Cc: r-help
Subject: Re: [R] normality tests [Broadcast]
From: [EMAIL PROTECTED]
On 25/05/07, Frank E Harrell Jr [EMAIL PROTECTED] wrote:
[EMAIL PROTECTED] wrote:
Hi all,
apologies for seeking advice on a general stats question. I ve run
normality tests using 8 different methods:
- Lilliefors
- Shapiro-Wilk
- Robust Jarque Bera
- Jarque Bera
- Anderson-Darling
- Pearson chi-square
- Cramer-von Mises
- Shapiro-Francia
All show that the null hypothesis that the data come from a normal
distro cannot be rejected. Great. However, I don't think
it looks nice
to report the values of 8 different tests on a report. One note is
that my sample size is really tiny (less than 20
independent cases).
Without wanting to start a flame war, are there any
advices of which
one/ones would be more appropriate and should be reported
(along with
a Q-Q plot). Thank you.
Regards,
Wow - I have so many concerns with that approach that it's
hard to know
where to begin. But first of all, why care about
normality? Why not
use distribution-free methods?
You should examine the power of the tests for n=20. You'll probably
find it's not good enough to reach a reliable conclusion.
And wouldn't it be even worse if I used non-parametric tests?
I believe what Frank meant was that it's probably better to use a
distribution-free procedure to do the real test of interest (if there is
one) instead of testing for normality, and then use a test that assumes
normality.
I guess the question is, what exactly do you want to do with the outcome
of the normality tests? If those are going to be used as basis for
deciding which test(s) to do next, then I concur with Frank's
reservation.
Generally speaking, I do not find goodness-of-fit for distributions very
useful, mostly for the reason that failure to reject the null is no
evidence in favor of the null. It's difficult for me to imagine why
there's insufficient evidence to show that the data did not come from a
normal distribution would be interesting.
Andy
Frank
--
Frank E Harrell Jr Professor and Chair School
of Medicine
Department of Biostatistics
Vanderbilt University
--
yianni
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